Problem: Solve for $x$ and $y$ using substitution. ${6x+6y = 6}$ ${y = -6x-4}$
Solution: Since $y$ has already been solved for, substitute $-6x-4$ for $y$ in the first equation. ${6x + 6}{(-6x-4)}{= 6}$ Simplify and solve for $x$ $6x-36x - 24 = 6$ $-30x-24 = 6$ $-30x-24{+24} = 6{+24}$ $-30x = 30$ $\dfrac{-30x}{{-30}} = \dfrac{30}{{-30}}$ ${x = -1}$ Now that you know ${x = -1}$ , plug it back into $\thinspace {y = -6x-4}\thinspace$ to find $y$ ${y = -6}{(-1)}{ - 4}$ $y = 6 - 4$ $y = 2$ You can also plug ${x = -1}$ into $\thinspace {6x+6y = 6}\thinspace$ and get the same answer for $y$ : ${6}{(-1)}{ + 6y = 6}$ ${y = 2}$